This invention relates to pneumatic tires and more particularly to a new and improved safety tire for use in run-flat condition and to self-sealing tires. When a conventional tire is without inflation air, the opposite interior walls of the tire come into contact with the localized pressure of the wheel toward the pavement, causing a severe flexing and buckling action to the cord fabric and the adjacent rubber compounds. Such very high stresses cause a heat build-up and a corresponding failure of the tire. In addition, the tire may be separate from the rim impairing the driver's ability to maintain control of the vehicle.